Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian
The authors describe an algorithm for computing the Selmer group of an isogeny between Abelian varieties. This algorithm applies when there is an isogeny from the image Abelian variety to the Jacobian of a curve [see also \textit{E. F. Schaefer}, Math. Ann. 310, 447--471 (1998; Zbl 0889.11021)], and extends the set of tools we have for computing Selmer groups. The use of auxiliary Jacobian simplifies the determination of locally trivial cohomology classes. As an application, they compute the Mordell-Weil group \(J_C(\mathbb Q)\) (where \(C\) denotes the smooth plane curve \(x^4+ (y^2+ 1)(x+ y)= 0\)) and use a Chabauty argument to determine the set \(C(\mathbb Q)\).
scientific article; zbMATH DE number 5009842